Communication systems have long transmitted digital signals using various carrier modulation techniques. The spectrum of a digital signal can be controlled and made compact by envelope filtering or phase domain filtering. An efficient phase domain filtering approach controls the signal spectrum by frequency modulating the filtered signal onto a carrier frequency to form a continuous phase modulated (CPM) signal. Because the CPM signal has a constant envelope, a power amplifier can be operated at maximum output power without affecting the spectrum of the filtered signal. Gaussian minimum shift keying (GMSK) is a form of continuous phase modulation. GMSK uses CPM signals with a constant signal envelope and a spectrum that can be made compact with the appropriate choice of the signal bandwidth bit time product (BT) product.
An M-ary GMSK signal is defined by its complex envelope described in terms of symbol energy E, symbol period T, carrier phase .theta..sub.c and phase modulation .theta.(t) using a modulation index h. Input data is formatted into data symbols prior to carrier modulation and transmission. The data formatting may be non-return to zero (NRZ) formatting. Equally probable NRZ data symbols belong to an M-ary alphabet of symbols having the symbol time T. The M-ary symbols are used to phase modulate a carrier reference. The GMSK phase response .theta.(t) originates from a Gaussian filter response g(t) of a Gaussian smoothing filter with a single sided 3 dB bandwidth B, truncated to an intersymbol interval duration L, that is a memory truncation length L. The GMSK Gaussian filter with a memory truncation length L of a GMSK signal is defined by the BT bandwidth bit time product, where B is the single sided 3 dB filter bandwidth in hertz. The Gaussian filter with a small BT product, has a memory length L equal to 1/BT. The Gaussian filter response g(t) used to phase modulate the carrier by a phase modulator having a modulation index h. In general, lowering the modulation index h while keeping the BT product constant will further reduce the spectral occupancy. The intersymbol memory length L is the number of elapsed symbol periods for the GMSK signal to accrue a complete phase change amount due to a single input symbol and hence represents the memory of the GMSK signal. The phase modulated GMSK signal is transmitted to GMSK receiver for communicating the input data stream.
The GMSK receiver demodulates the received GMSK signal into a demodulated signal that is in turn passed through Laurent filters providing filter signals fed into a Viterbi decoder for providing a estimate of the input data stream. The Laurent filters are applied to an accumulated phase at a current bit time. The current bit has signal components extending over L bit periods. A typical coherent receiver for M-ary GMSK signal is based on a pulse amplitude modulation (PAM) representation of CPM signals using Laurent filtering, and employs the Viterbi algorithm to optimally demodulate symbol sequences. In demodulating M-ary GMSK signals using the Viterbi algorithm, a differential decoder has been necessary to resolve data bit ambiguities while providing a nominal bit error rate (BER) that is desirably as small as practicable. A Viterbi algorithm typically employs a sliding window in the demodulation process where the width of the sliding window represents the demodulation memory or delay. The surviving state sequence produced by the sliding window Viterbi algorithm at stage n depends on all the demodulated symbols d.sub.n (t). The intrinsic data dependency of the survivor sequences a.sub.n (t) disadvantageously requires a differential decoder operation in the receiver when deciding on the actual demodulated symbol from successive survivors of the Viterbi algorithm resulting in a differential bit error rate degradation.
In the related application, Nguyen et. al., an improved GMSK timing recover loop offers closed loop generation of a data timing signal at a baseband frequency. The improved GMSK timing recovery loop enables recovery of the transmitted data using the baseband data timing signal .tau.(t) with high accuracy at low bit signal to noise ratio (BSNR) and at a small BT product, and has the advantage of negligible loss due to non-random data patterns. Another advantage associated with GMSK timing recovery loop is the adoption of the well known digital transition tracking loop (DTTL) used in M-ary PSK systems with a modification of adding a hard limiter in closed loop control of the data timing signal.
The GMSK system includes the transmitter modulator and the receiver demodulator between which is transmitted the GMSK signal. The demodulator includes a carrier tracking loop for providing a GMSK demodulated received signal R.sub.o (t) and the bit timing recovery loop for providing the bit timing signal .tau.(t). The carrier tracking loop preferably employs reverse modulation. The GMSK timing recovery loop performance employs the hard limiter adjusted by a bit timing error signal for improved insensitivity to the values of BT while operating at low BSNR. The GMSK timing recovery loop takes advantage of the observation that the cosine of the baseband GMSK signal has zero crossings at multiples of the bit duration. The hard limiter is used to create the clocking signal for the NRZ data stream that has the zero crossings at multiples of the bit duration. The digital transition tracking loop is then used to track the zero crossings of the NRZ data stream clocking signal from the received demodulated GMSK signal, and the bit timing signal .tau.(t) is then generated by the DTTL with less jitter for improved data detection. In the GMSK timing recovery loop, the hard limiter is adjusted by the bit timing error signal .tau..sub.e (t) to reduced jitter in clock sampling of the NRZ data stream. Hence, the digital transition tracking loop tracks the adjusted zero-crossings of the NRZ data stream, and the reduced jitter bit timing signal .tau.(t) is then generated for accurate data sampling and detection. Significantly, this timing recovery loop is operated at baseband and is a preferred improvement to the GMSK receiver.
In the related application, Lui et. al., a data preceding algorithm is implemented prior to modulation in the transmitter to substantially improve the resulting BER performance of the continuous phase modulated (CPM) transmitters and receivers, such as the Gaussian minimum shift keying (GMSK) transmitters and receivers without the use of differential decoders while preserving the spectral occupancy the GMSK signals. The preceding algorithm encodes the source NRZ data symbols prior to the GMSK modulation so that the cumulative phase of the precoded symbols becomes the absolute phase of the data symbols in the signal phase trellis of the Viterbi algorithm. The preceding algorithm offers performance improvement for M-ary coherently demodulated GMSK signals.
Precoding improves the BER performance for coherent demodulation of the M-ary GMSK signals implemented using a pulse amplitude modulated signal subject to the Viterbi algorithm. The preceding algorithms encodes the source NRZ data symbols d.sub.n (t) prior to the GMSK modulation so that the cumulative phase of the precoded symbols d.sub.n (t) is identical to the exact phase of the source NRZ symbols at every stage of the Viterbi algorithm. In the Viterbi algorithm, the preceding process produces a set of survivor sequences for estimating the original data bit without the use of differential decoding. The Gaussian filter can be expressed mathematically, and the Laurent mathematical expansion dictates the matched filter bank. Without preceding, the Gaussian filter creates phase ambiguities that are resolved by differential decoding. Because the precoded symbols have the same statistics as the source symbols, the transmit spectrum of the GMSK signal is preserved while eliminating the need for differential decoding. Depending upon the channel bit error rate in operation, the precoding method will render a signal to noise ratio (SNR) improvement of 3 dB over the same modem that demodulates GMSK signals without preceding.
The carrier phase demodulation of the received signal has long been performed at high intermediate frequencies (IF) causing squaring signal losses and consuming high power when demodulating at the IF frequencies. The squaring losses disadvantageously increase the bit error rate. The techniques used for carrier phase synchronization usually require squaring or Costas loops with losses due to squaring, and self noise due to intersymbol interference (ISI) with high BER. These carrier tracking loops do not perform well in the presence of non-random data patterns where the discrete components for carrier recovery may vanish.
A reverse modulation method may be used in carrier phase tracking loops operating at high intermediate frequencies. The reverse modulation method works very well with differentially encoded data. However, when used with the precoded data, the tracking performance becomes unstable and sensitive to the loop gain. Additionally, when operating at high intermediate frequencies, more power is disadvantageously consumed. While prior GMSK systems have used preceding to avoid receiver differential decoding, the precoded data absolute phase characteristics have not been used for baseband operation of a carrier tracking loop. These and other disadvantages are solved or reduced using the invention.